Given the overlapping impact of the Factory Act of 1833 and the Elementary Education Act 1876, it is possible that the certificate would serve both purposes. It would show that he could be employed (because he was over 8) and that he was to continue to receive (part-time) education (since he was under 14).
The following comes from The Registrar General's Supplementary Instructions to Registration Officers, 1926 (p 44):
In order to assist Registration Officers in determining whether the
case in which an applicant applies for a Certificate of Birth under
the Elementary Education or Factory and Workshop Act is applicable
under those Acts, the following short list of cases has been drawn up
in which the Registrar-General has decided that Certificates, under
the Acts referred to, should be issued. Registration Officers must,
however, clearly understand that the list is only intended to serve as
a help, and it must not be considered as a complete list of applicable
Purpose for which Certificate is required:—
- To effect the removal of a child from an Elementary School to an Industrial School or a Reformatory.
- To enable a child in an Elementary School to be apprenticed as a Pupil Teacher.
- To enable a boy to attend an examination for the situation of Dockyard Apprentice or Engineer Student.
- To enable a boy to enter the service of the General Post Office as Telegraph Messenger.
- To enable a boy to enter the Stamping Department of the Inland Revenue, Somerset House.
- To prove the age of a child taking part in a Pantomime or other entertainment in a Theatre or Music Hall.
- For admission to an Orphanage or other Charitable Institution in which Elementary Education is given.
- For admission to a School of Domestic Economy.
With regard to candidates for Scholarships under the Technical
Education Acts, the Registrar-General has obtained the opinion of the
Law Officers of the Crown, who have decided that the candidates are
not entitled to the cheap Certificates under the above Act. Such
Certificates are not, in the opinion of the Law Officers, required
"for any purpose connected with Elementary Education," the purposes
referred to being those arising out of the administration of the
Elementary Education Acts.
A cheap Certificate is also held not to be claimable for the purposes
of Football Matches or other Athletic Competitions.
Note.—The Registrar-General is advised that cheap Birth Certificates
under the Elementary Education Act are available for the purposes of
Junior County Exhibitions or of Higher Elementary Education.